# Tuddenham and Snyder obtained the following results for 6

Tuddenham and Snyder obtained the following results for 66 California boys at ages 6 and 18 (the scatter diagram is football-shaped):
average height at $$6 \approx 3$$ feet 10 inches, $$SD \approx 1.7$$ inches
average height at $$18 \approx 5$$ feet 10 inches, $$SD \approx 2.5$$ inches, $$r \approx 0.80$$
a) Find the r.m.s. error for the regression prediction of height at 18 from height at 6. b) Find the r.m.s. error for the regression prediction of height at 6 from height at 18.

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$$\sqrt{(1-r^{2})} \cdot SD_{y}$$
a) The r.m.s. error for the regression prediction of height at 18 from height at 6: in this case:
$$\sqrt{1-0.8^2} \cdot 2.5 = \sqrt{1-0.64} \cdot 2.5 = \sqrt{0.36} \cdot 2.5 = 0.6 \cdot 2.5 = 1.5$$
b) The r.m.s. error for the regression prediction of height at 6 from height at 18:
$$\sqrt{1-0.8^2} \cdot 1.7 = \sqrt{1-0.64} \cdot 1.7 = \sqrt{0.36} \cdot 1.7 = 0.6 \cdot 1.7 = 1.02$$